Method for the reconstruction of three-dimensional objects

ABSTRACT

The invention relates to a method for the computer-aided reconstruction of a three-dimensional anatomical object ( 3 ) from diagnostic image data. First of all, a diagnostic image data set of the object ( 3 ) is acquired. Then a seed point ( 5 ) is set, starting from which the object is reconstructed within a reconstruction volume ( 4 ). Thereafter, an adjacent point of the reconstruction volume ( 4 ) likewise belonging to the object ( 3 ) is located in accordance with a propagation criterion, which is calculated by means of a mathematical analysis of local areas ( 6, 7 ), assigned to the point concerned, of the image data set Reconstruction of the three-dimensional structure of the object ( 3 ) is then performed within the reconstruction volume ( 4 ) by multiple repetition of this method step and propagation along the located adjacent points. To apply such a reconstruction method to image data obtained by means of rotational X-ray imaging, wherein a plurality of two-dimensional projection images ( 1, 2 ) are recorded from different projection directions, the invention proposes that the propagation criterion be calculated by subjecting the local image areas ( 6, 7 ) of the two-dimensional projection images ( 1, 2 ) in each case individually to the mathematical analysis.

The invention relates to a method for the computer-aided reconstructionof a three-dimensional anatomical object from diagnostic image data,having the method steps:

a) acquisition of a diagnostic image data set of an object,

b) setting of a seed point belonging to the object within areconstruction volume, c) location of an adjacent point, likewisebelonging to the object, within the reconstruction volume in accordancewith a propagation criterion, which is calculated by means of amathematical analysis of local areas, assigned to the point concerned,of the image data set,

d) reconstruction of the three-dimensional structure of the objectwithin the reconstruction volume by multiple repetition of method stepc) and propagation along the adjacent points thus located.

In addition, the invention relates to a computer program and an imagingapparatus with computer means for performing this method.

In the field of angiography, three-dimensional medical imaging methods,such as for example three-dimensional rotational X-ray imaging (3D-RX)or magnetic resonance imaging (MRI), are growing in importance. Thevolume image data obtained with such methods contain interestinginformation for diagnosis of vessel diseases, such as for examplestenoses or aneurysms. In such cases, visualization of the vesselstructures is crucial in allowing a doctor treating the condition torecognize quickly and reliably potential danger sources (e.g. animpending infarction or thrombosis).

Computer-aided three-dimensional reconstruction of the vessel system ofa patient from the image data acquired on the one hand allows theprofile of the blood vessels to be visualized with high reproductionaccuracy, anatomical structures not belonging to the vessel systemconcerned being hidden. On the other hand, the three-dimensionalreconstruction of the vessel structures is a useful aid in planninginterventions, such as for example left coronary catheter investigations(PTCA).

A three-dimensional reconstruction method for analyzing volume imagedata acquired by magnetic resonance angiography (MRA) is known forexample from an article by Young et al (S. Young, V. Pekar and J. Weese,“Vessel Segmentation for Visualization of MRA with Blood Pool ContrastAgent”, MICCAI 2001, 491-498, Utrecht, Oct. 2001). The previously knownmethod serves, inter alia, to separate the arterial and venous vesselsystems from one another during visualization of the image data.According to the previously known method, first of all a diagnosticimage data set is acquired in the form of a volume image of the vesselstructures of interest, using a suitable contrast agent. Then, a usersets a seed point within a reconstruction volume, this seed point beingidentified by the user as belonging to a venous vessel. Automaticthree-dimensional reconstruction of the selected vessel then takes placeby means of a propagation method, which is based on a mathematicalanalysis of the respective local image areas. Starting from the seedpoint, points within the reconstruction volume are identified, inaccordance with a propagation criterion supplied by the mathematicalanalysis, as belonging or not belonging to the vessel, wherebysegmentation of the reconstruction volume takes place. Propagationcontinues until the entire structure has been reconstructed or until aset end point is reached. The mathematical analysis applied forcalculation of the propagation criterion is of fundamental importance tothe previously known method. In the stated article, a mathematicalfilter is proposed in this respect, which is based on evaluation of thesecond derivatives of the gray scale values within the local imageareas. A proposed alternative involves adaptation of the local imagedata to a cylinder model, by means of which the mathematical analysis isrendered selective for image structures typical of blood vessels.

In rotational X-ray imaging, a plurality of two-dimensional projectionimages is recorded at different projection angles, for example by meansof a C-arm X-ray apparatus. To make the blood vessels of the patientunder investigation visible in the projection images, an X-ray absorbentcontrast agent is injected into the patient. A problem with thisinvestigation method is that the blood vessels typically have acomplicated three-dimensional profile, which it is difficult for thedoctor to detect solely on the basis of two-dimensional projectionimages. The missing three-dimensional information within a projectionimage must be added by the doctor by comparison with images recorded atother projection angles.

It is now possible to generate a volume image data set from theplurality of two-dimensional projection images recorded by means of3D-RX using suitable modeling or back projection methods on a suitablecomputer. This volume image data set may then undergo an analysis of thetype outlined above for the purpose of reconstruction of thethree-dimensional vessel structures. This procedure, however, isdisadvantageously associated with considerable computing power. Afurther disadvantage is that, in particular if the coronary vessels ofthe patient are to be investigated, generation of the projection imageshas to be ECG-controlled, so that the coronary arteries are recorded inall the images in the same phase of the heart beat cycle. Because of theneed for ECG control, only a comparatively small number of images isthen available for each phase of the heart beat cycle, which means thatthe volume images reconstructed therefrom reproduce the vesselstructures only relatively inaccurately. A quantitative analysisaccording to the above-described reconstruction method does not thenprovide any usable results.

Taking this as basis, it is an object of the present invention toprovide a method of segmenting a reconstruction volume which is in aposition, starting from a comparatively small number of two-dimensionalprojection images, to determine the three-dimensional structure of theobject reliably, precisely and using as little computing power aspossible.

In the case of a method of the above-mentioned type, this object isachieved according to the invention in that, in method step a), aplurality of two-dimensional projection images is recorded fromdifferent projection directions, the propagation criterion beingcalculated in method step c) by subjecting the local image areas of thetwo-dimensional projection images in each case individually tomathematical analysis.

The basic concept of the invention is to perform the computer-aidedsegmentation of the reconstruction volume directly by means of apropagation method known per se, without any intermediate reconstructionof a three-dimensional volume image data set from the projection images.In the process, propagation in the reconstruction volume along thecontours of the object to be reconstructed is controlled by combiningthe information obtained by means of the mathematical analysis appliedto the individual two-dimensional projection images to yield a uniformpropagation criterion.

To this end, it is possible, for example, to identify a point in methodstep c) as belonging to the object, provided that the mathematicalanalysis yields a result which agrees for a plurality of two-dimensionalprojection images. This procedure takes account of the fact that, on thebasis of projection, the mathematical analysis of an individual,two-dimensional projection image may cause the point concerned to appearto belong to the object even when this is not actually the case. Only acomparison with the results obtained by mathematical analysis of theother projection images in relation to this point allows reliablesegmentation.

The local image areas are appropriately determined in method step c) byprojecting the point concerned within the reconstruction volume inaccordance with the respective projection directions into the imageplanes of the two-dimensional projection images. In this way, thegeometric conditions when the projection images are recorded arereplicated, in order to be able to achieve assignment of the points ofthe reconstruction volume and the image points of the two-dimensionalprojection images.

By the mathematical analysis in method step c), a propagationcoefficient ought appropriately to be calculated in each case aspropagation criterion for each two-dimensional projection image, thevalue of which coefficient indicates whether the point concerned belongsto the object or not. Such a coefficient is particularly well suited toperformance of the method according to the invention by means of acomputer, since location of points belonging to the object to bereconstructed may be effected by simple numerical comparison. Forexample, the procedure may be performed in such a way that, in methodstep c), a point is identified as belonging to the object, provided thatthe propagation coefficient assumes a large value for-a plurality oftwo-dimensional projection images.

A characteristic of blood vessels is their axial symmetry. They extend along way in one direction and only a short way in the directionperpendicular thereto. This morphological characteristic may be usedaccording to the invention to calculate the propagation coefficient. Forthree-dimensional reconstruction of vessel structures, it is accordinglysensible, during calculation of the propagation coefficient, tocalculate the inherent values of the Hesse matrix of the gray scalevalues in the local image area of the respective two-dimensionalprojection image. By evaluating these inherent values, propagation thenfollows the image structures with—from a spatial point of view—thelowest possible gray scale curvature values, because the Hesse matrixprovides information about the local second derivatives of the grayscale values. Suitable formulae for calculating the propagationcoefficient on the basis of the inherent values of the Hesse matrix maybe found, for example, in the above-cited article by Young et al. Thepropagation coefficient may be calculated from the two-dimensionalprojection images for example as follows:${R\left( \overset{\rightarrow}{x} \right)} = \left\{ {{{\begin{matrix}0 & {,{{\lambda_{2}\left( \overset{\rightarrow}{x} \right)} > 0},} \\{\exp\left\{ {- \frac{r_{\alpha}^{2}}{2\quad\alpha^{2}}} \right\}\left( {1 - {\exp\left\{ {- \frac{S^{2}}{2c^{2}}} \right\}}} \right)} & {,{{\lambda_{2}\left( \overset{\rightarrow}{x} \right)} \leq 0},}\end{matrix}\quad r_{\alpha}} = \frac{\lambda_{1}}{\lambda_{2}}},{S = {{\sqrt{\sum\limits_{l}\lambda_{l}^{2}}.{in}}\quad{which}}}} \right.$

In this equation, a and c are weighting factors and λ₁ ({overscore (x)})and λ₂ ({overscore (x)}) are the inherent values of the local gray scalevalue Hesse matrix calculated at the point {overscore (x)} within therespective two-dimensional projection image. More details about this maybe found in the above-cited publication by Young et al.

When calculating the propagation coefficient for the respectivetwo-dimensional projection image, adaptation to a cylinder model withinthe local image area may also be calculated. Such a cylinder model,which is also described in detail in the stated article by Young et al,likewise makes vessel structures distinguishable from other anatomicalstructures.

Reconstruction is appropriately stopped when a predeterminable end pointis reached during propagation in method step d). Such an end point mayeither be predetermined interactively or determined automatically, forexample on the basis of the size of the reconstruction volume.

An imaging apparatus, in particular a C-arm X-ray apparatus, forperforming the method according to the invention constitutes the subjectmatter of claim 9, according to which a computer means of the imagingapparatus is provided with a program such that the two-dimensionalprojection images are recorded according to the above-described method.For angiographic investigations of the coronary arteries, the imagingapparatus appropriately comprises ECG control as claimed in claim 10, soas to be able to record the projection images synchronously with theheart beat.

A computer program as claimed in claim 11 is suitable for performing themethod according to the invention, for example on an imaging apparatusequipped with a suitable computer means. The software required thereforemay be made available to the users of corresponding imaging apparatusadvantageously on a suitable data medium, such as a floppy disk or aCD-ROM, or by downloading from a data network (Internet).

The invention will be further described with reference to examples ofembodiments shown in the drawings to which, however, the invention isnot restricted. In the Figures:

FIG. 1 is a schematic representation of the method according to theinvention for reconstructing a three-dimensional anatomical object;

FIG. 2 shows an imaging apparatus according to the invention.

FIG. 1 shows a diagnostic image data set consisting of twotwo-dimensional projection images 1, 2, which image data set wasacquired by means of X-ray fluoroscopy. Each of the projection images 1,2, recorded at different projection angles, shows a branched bloodvessel 3 of a patient. The projection images 1, 2 accordingly show thesame blood vessel 3 from different perspectives. To acquire the imagedata set, a contrast agent was administered to the patient, such thatthe blood vessel 3 shows up dark in the projection images. Toreconstruct the three-dimensional structure of the blood vessel 3according to the invention, a seed point 5 is firstly set within areconstruction volume 4. The contour of the blood vessel 3 is thenreconstructed in the volume 4, by locating adjacent points in the volume4 in each case belonging to the blood vessel 3 in accordance with apropagation criterion. To this end, local image areas 6 and 7 belongingto the respective point 5 within the two-dimensional projection images 1and 2 respectively are in each case subjected individually tomathematical analysis. After location of a point adjacent to the seedpoint 5, the procedure is repeated for points in turn adjacent to thispoint, until the entire structure of the blood vessel 3 has beenreconstructed within the volume 4. The point investigated in each casewith each propagation step is identified as belonging to the bloodvessel if the mathematical analysis of the local image areas 6 and 7gives a positive result for both projection images 1 and 2 respectively.The local image areas 6 and 7 are determined by projecting the point 5,in accordance with the projection directions in which the two images 1and 2 were recorded, into the image planes of these two images. This isindicated in FIG. 1 by arrows 8 and 9.

The imaging apparatus illustrated in FIG. 2 is a C-arm X-ray apparatus,which comprises a C-arm 10, which is suspended by means of a holder 11from a ceiling (not described in any more detail). An X-ray source 12and an X-ray image converter 13 are guided movably on the C-arm 10, suchthat a plurality of two-dimensional projection X-ray images of a patient15 lying on a table 14 in the center of the C-arm 10 may be recorded atdifferent projection angles. Synchronous movement of the X-ray source 12and the X-ray image converter 13 is controlled by a control unit 16.During image recording, the X-ray source 12 and the X-ray imageconverter 13 travel synchronously around the patient 15. The imagesignals generated by the X-ray image converter 13 are transmitted to acontrolled image processing unit 17. The heart beat of the patient 15 ismonitored using an ECG apparatus 18. The ECG apparatus 18 transmitscontrol signals to the image processing unit 17, such that the latter isin a position to store a plurality of two-dimensional projection imagesin each case in the same phase of the heart beat cycle, in order in thismanner to perform an angiographic investigation of the coronaryarteries. The image processing unit 17 comprises a program control, bymeans of which three-dimensional reconstruction of a blood vesseldetected with the image data set thus acquired is performed, accordingto the above-described method. The reconstructed blood vessel may thenbe visualized in known manner on a monitor 19 connected to the imageprocessing unit 17.

1. A method for the computer-aided reconstruction of a three-dimensionalanatomical object (3) from diagnostic image data, having the methodsteps: a) acquisition of a diagnostic image data set of the object (3),b) setting of a seed point (5) belonging to the object (3) within areconstruction volume (4), c) location of an adjacent point, likewisebelonging to the object (3), within the reconstruction volume (4) inaccordance with a propagation criterion, which is calculated by means ofa mathematical analysis of local image areas (6, 7), assigned to thepoint (5) concerned, of the image data set, d) reconstruction of thethree-dimensional structure of the object (3) within the reconstructionvolume (4) by multiple repetition of method step c) and propagationalong the adjacent points thus located, characterized in that, in methodstep a), a plurality of two-dimensional projection images (1, 2) isrecorded from different projection directions, the propagation criterionbeing calculated in method step c) by subjecting the local image areas(6, 7) of the two-dimensional projection images (1, 2) in each caseindividually to the mathematical analysis.
 2. A method as claimed inclaim 1, characterized in that, in method step c), a point is identifiedas belonging to the object (3) if the mathematical analysis yields aresult which agrees for a plurality of the two-dimensional projectionimages (1, 2).
 3. A method as claimed in claim 1, characterized in that,in method step c), the local image areas (6, 7) are determined byprojecting the respective point (5) within the reconstruction volume (4)in accordance with the respective projection directions into the imageplanes of the two-dimensional projection images (1, 2).
 4. A method asclaimed in claim 1, characterized in that, a propagation coefficient iscalculated by the mathematical analysis in method step c), as apropagation criterion for each two-dimensional projection image (1, 2),the value of which coefficient indicates whether the point (5) concernedbelongs to the object or not.
 5. A method as claimed in claim 4,characterized in that, during calculation of the propagationcoefficient, the inherent values are calculated of the Hesse matrix ofthe gray scale values in the local image area (6, 7) of the respectivetwo-dimensional projection image (1, 2)
 6. A method as claimed in claim4, characterized in that, when calculating the propagation coefficientfor the respective two-dimensional projection image (1, 2), anadaptation to a cylinder model within the local image area (6, 7) iscalculated.
 7. A method as claimed in claim 4, characterized in that apoint is identified in method step c) as belonging to the object (3) ifthe propagation coefficient assumes a large value for a plurality oftwo-dimensional projection images (1, 2).
 8. A method as claimed inclaim 1, characterized in that the reconstruction is stopped when apredeterminable end point is reached during propagation in method stepd).
 9. An imaging apparatus, in particular a C-arm X-ray apparatus,having means (10, 11, 12, 13, 16) for generating an image data set,which set comprises a plurality of two-dimensional projection images ofa body part of a patient (15) recorded from different projectiondirections, and having computer means (17) for reconstructing athree-dimensional anatomical object from the image data set,characterized in that the computer means (17) comprise a program controlwhich operates according to the method as claimed in claim 1 toreconstruct the object.
 10. An imaging apparatus as claimed in claim 9,characterized by an ECG control (18), by means of which recording of thetwo-dimensional projection images can be controlled in accordance withthe heart beat cycle of the patient (15).
 11. A computer program for animaging apparatus in particular a C-arm X-ray apparatus, having means(10, 11, 12, 13, 16) for generating an image data set, which setcomprises a plurality of two-dimensional projection images of a bodypart of a patient (15) recorded from different projection directions,and having computer means (17) for reconstructing a three-dimensionalanatomical object from the image data set, characterized in that thecomputer means (17) comprise a program control which operates accordingto the method as claimed in one of claims 1 to 8 to reconstruct theobject, characterized in that the method as claimed in claim 1 isimplemented by the computer program on the computer means of the imagingapparatus.